Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap

Hiroyuki Yoshimoto; Susumu Kurihara

doi:10.1088/0305-4470/36/42/004

Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap

Hiroyuki Yoshimoto^*, Susumu Kurihara

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground-state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that the Thomas-Fermi approximation agrees well with the exact results for any dimension even though the system is small. In the high-temperature (classical) region, we find the interaction energy decreases in proportion to T^-d/2, where T is the temperature and d is the dimension of the system.

Original language	English
Pages (from-to)	10461-10470
Number of pages	10
Journal	Journal of Physics A: Mathematical and General
Volume	36
Issue number	42
DOIs	https://doi.org/10.1088/0305-4470/36/42/004
Publication status	Published - 2003 Nov 24

ASJC Scopus subject areas

Physics and Astronomy(all)
Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1088/0305-4470/36/42/004

Cite this

@article{f57e4435a979479c94f8db682d027525,

title = "Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap",

abstract = "We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground-state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that the Thomas-Fermi approximation agrees well with the exact results for any dimension even though the system is small. In the high-temperature (classical) region, we find the interaction energy decreases in proportion to T-d/2, where T is the temperature and d is the dimension of the system.",

author = "Hiroyuki Yoshimoto and Susumu Kurihara",

year = "2003",

month = nov,

day = "24",

doi = "10.1088/0305-4470/36/42/004",

language = "English",

volume = "36",

pages = "10461--10470",

journal = "Journal of Physics A: Mathematical and General",

issn = "0305-4470",

publisher = "IOP Publishing Ltd.",

number = "42",

}

TY - JOUR

T1 - Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap

AU - Yoshimoto, Hiroyuki

AU - Kurihara, Susumu

PY - 2003/11/24

Y1 - 2003/11/24

N2 - We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground-state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that the Thomas-Fermi approximation agrees well with the exact results for any dimension even though the system is small. In the high-temperature (classical) region, we find the interaction energy decreases in proportion to T-d/2, where T is the temperature and d is the dimension of the system.

AB - We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground-state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that the Thomas-Fermi approximation agrees well with the exact results for any dimension even though the system is small. In the high-temperature (classical) region, we find the interaction energy decreases in proportion to T-d/2, where T is the temperature and d is the dimension of the system.

UR - http://www.scopus.com/inward/record.url?scp=0242382572&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242382572&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/42/004

DO - 10.1088/0305-4470/36/42/004

M3 - Article

AN - SCOPUS:0242382572

SN - 0305-4470

VL - 36

SP - 10461

EP - 10470

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 42

ER -

Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this